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5.6 Exponents and Scientific Notation

5.6 Exponents and Scientific Notation. Properties of Exponents. 2 3 · 2 5. = (2 · 2 · 2) (2 · 2 · 2 · 2 · 2). = 2 8. 3 4 · 3 7. = (3 · 3 · 3 · 3) (3 · 3 · 3 · 3 · 3 · 3 · 3). = 3 11. Rule 1 for exponents: b m · b n = b m + n.

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5.6 Exponents and Scientific Notation

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  1. 5.6 Exponents and Scientific Notation

  2. Properties of Exponents 23 · 25 = (2 · 2 · 2) (2 · 2 · 2 · 2 · 2) = 28 34 · 37 = (3 · 3 · 3 · 3) (3 · 3 · 3 · 3 · 3 · 3 · 3) = 311 Rule 1 for exponents: bm · bn = bm+n The base number is b and the exponents are m and n. To multiply, if the base numbers are the same, add the exponents. 513 · 54 = 517 712 · 713 = 725 34714 · 34741 = 34755

  3. Properties of Exponents Rule 2 for exponents: (bm)n = bmn The base number is b and the exponents are m and n. To raise an exponential expression to a power, multiply the exponents.

  4. Properties of Exponents Rule 3 for exponents: To divide, if the base numbers are the same, subtract the exponent in the denominator from the exponent in the numerator. Any non zero number raised to the zero power will be 1.

  5. Properties of Exponents Rule 4 for exponents: A negative exponent in the numerator will become positive if the number is moved to the denominator. (A negative exponent in the denominator will become positive if it is moved to the numerator.)

  6. Properties of Exponents Rule 1 for exponents: bm · bn = bm+n Rule 2 for exponents: (bm)n = bmn Rule 3 for exponents: Rule 4 for exponents:

  7. Properties of Exponents Rule 1 for exponents: bm · bn = bm+n Rule 2 for exponents: (bm)n = bmn Rule 3 for exponents: Rule 4 for exponents:

  8. Scientific Notation A number is written in scientific notation when it is expressed in the form a× 10n, when the absolute value of a is greater than or equal to 1 and less than 10 and n is an integer (a will have exactly one non-zero digit to the left of the decimal point.) Standard notation Scientific notation The exponent on the 10 indicates how many places the decimal point is moved. Scientific notation is useful for writing large and small numbers. Standard notation Scientific notation

  9. Scientific Notation A number is written in scientific notation when it is expressed in the form a× 10n, when the absolute value of a is greater than or equal to 1 and less than 10 and n is an integer (a will have exactly one non-zero digit to the left of the decimal point.) The exponent on the 10 indicates how many places the decimal point is moved.

  10. Calculations with Scientific Notation

  11. Calculations with Scientific Notation

  12. And now a little history. Multiplication with exponents is easy. Addition can be very tricky. In 1637 Pierre de Fermat wrote in a mathematics book that he was reading, “I have a truly marvelous proof of this proposition which this margin is too narrow to contain.” The proposition was that there could be no an+bn= cn if a, b, and c are integers and n is an integer greater than 2. In 1989 an episode of Star Trek aired with a scene where Captain Picard is doing mathematics for recreation. He is trying to find a proof for Fermat’s Last Theorem. The theorem is 800 years old and still unproven according to Picard. In 1993 Andrew Wiles found a proof for the theorem. It certainly would not fit in the margin of a book. The proof fills 109 pages. He spent seven years of his life working on the problem.

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